In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does ...

Finitely generated abelian... · Category:Abelian group theory · Non-abelian group

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same ...

Lattice theory studies free abelian subgroups of real vector spaces. In algebraic topology, free abelian groups are used to define chain groups, and in ...

So, finitely generated abelian groups can be thought of as a generalization of cyclic groups. Every finite abelian group is finitely generated. The finitely ...

For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup. Torsion ...

, a group in which the binary operation is commutative. Category of abelian groups (Ab), has abelian groups as objects and group homomorphisms as morphisms.

In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category: indeed ...